I would be lying if I said I wasn't concerned but I do see differences between the states that are experiencing unrest and those that are not (e.g. Qatar and UAE). The common threads in those countries with disturbances are that there is often a religious divide and/or a deal of financial inequality. Oppressive presidential dicatorship hasn't helped.
Bahrain seems to have most of these issues - a Shi'a majority ruled by a Sunni minority that seems to keep the best of everything for themselves (jobs, money, status). Yemen, Libya, Egypt, Tunisia all have/had presidential systems that were so corrupt that they would have been laughable if they weren't so saddening - when added to endemic corruption and inequality the result is inevitable.
Qatar and the UAE seem to be in a better position in many respects. The money is shared out much more evenly and the religious make up of the majority of the population matches that of the rulers - approximately 80% Sunni in both cases, coupled with a greater degree of religious freedom (e.g. Christian churches and the like are permitted and their rights enshrined in the constitution). The media here in the UAE are also freely reporting the events in other countries - unlike the attempts by Libya and the like to suppress comment, a pointless exercise in these days of the internet.
Ghaddafi is on the skids - it's just a matter of time before he goes the way of the others and his "end" may be more like that of Nicolae Ceaucescu than that of Hosni Mubarak. Saleh in yemen really ought to be packing his bags and nipping off to China or South America before he finds himself backed into a corner from which there is no escape.
However, I would be very surprised indeed if Qatar and the UAE were to experience the same degree of unrest. Although the earlier post about Qatar "protests" was made with tongue in cheek, it actually sums up the situation rather well. OK, so there's no real democracy here but Qataris and Emiratis have got such a good deal in life that there is nothing to be gained from making a fuss - quite the reverse in fact. On the other hand, a Bahraini Shi'ite may well feel that he has nothing to lose, especially when in the company of a good number of his subjugated compatriots.
In short, I'm not expecting to be leaving the country any time soon.
I may be reading this all wrong but I can't see what the average Qatari or Emirati would have to gain, in fact I can only see them losing out. The story in Yemen, Libya, Egypt and Bahrain is quite different.